Question

given f(x)= 5x+4/5x^2+4x and g(x) = 1/x

a. determine the domains of f(x) and g(x)
b. simplify f(x) and find any vertical asymptotes
c. explain how the two functions differ

I have absolutely no idea how to answer this question - can you please help me to figure it out?!

Answer 1

If you really have no idea, you must not have looked at the material given you...

the domain of any rational function is where the denominator is zero

5x^2+4x = x(5x+4). so,
the domain of f is all reals except x = 0 or -4/5
the domain of g is all reals except x=0

I think you can simplify f(x).
Vertical asymptotes are where the denominator is zero and the numerator is not zero.

f(x) = 1/x except where x = -5/4
g(x) = 1/x
both are undefined at x=0